Method of adaptive thread

ABSTRACT

A method of finish mill adaptive thread is described wherein an observed error in per unit draft at an upstream stand is compensated in the remaining active downstream stands of the mill by changing the per unit draft of the downstream stands by an amount proportional to the original per unit draft of each stand. Preferably, the percentage of draft change in the downstream stands is determined implicitly by solution of an error equation which defines the necessary relationship between the observed error and controllable variables within the mill. Because the relative drafting pattern between downstreams stands of the mill remains substantially unchanged, the delivery stand normally receives the smallest percentage of the total adjustment and the risk of exceeding restraining limits on any one stand is reduced.

METHOD OF ADAPTIVE THREAD June 4, 1974 ii? i t i v hr. .2 2.. Attorney, Agent, or Firm-Arnold E. Renner; Harold [75] Inventor: C. Michael Miglore, Scotia, N.Y.

H. Green, Jr. [73] Assignee: General Electric Company, Salem,

Va. I [57] ABSTRACT [22] Filed; 18, 97 A method of finish mill adaptive thread is described wherein an observed error in per unit draft at an up- [21] Appl' 315,815 stream stand is compensated in the remaining active downstream'stands of the mill by changing the per 52 us. CI. 72/16, 72/21 unit draft of the downstream Stands y an amount P 51 rm. CI B21b 37/02 Portional to the original p unit draft of each stand- [58] Field of Search 72/6-9, 10, Preferably, the Percentage of draft change in the 72 1 1 downstream stands is determined implicitly by solution of an error equation which defines the necessary 5 References Cited relationship between the observed'e'rror and controllable variables within the mill. Because the relative 3 5 3 PATENTS drafting pattern between downstreams stands of the ml r 3,5 742 80 4/197 smith, Jr'm 72/8 I mill remains substantially unchanged, the delivery 3 7'3 313 M973 5 radii 72/8 stand normally receives the smallest percentage of the p total adjustment and the risk of exceeding restraining limits on any one stand is reduced.

17 Claims, 5 Drawing Figures c FROM 0 TOC as: 1 SP3 to I FROM c Toe TOC s04 {R53 amt R94 5 DI15 0H3 0M4 H3 H4 :15 mm: FRO?" v T05 To c TOC o 5 FROM TO LCS w lill HIT A READE THlCKNESS im) m m WIDTH HARDNESS PA TEN'I'EII I 4 I974 DPUDFI(I)=PUDFAT- PO UT: (1)

SIIEEI 2 IIF 5 CALCULATE DEVIATION IN sTAND PER UNIT RAFT (MEASURED EXPECTED) cALcU ATE DEvIATIoN IN STAND PER UNIT DRAFT (SPEED-LIMITED VALUE -EXPECTED VALUE) ENTRY STAND YES POSITION INITIALIZE ACTIVE STAND COUNTER, ACTCN'I} WITH THE NUMBER OF ACTIVE STANDS FOR THIS PASS THRU FINISH DPUDFI (I) =PD1(I) -Po TI(r) ADAPTIVE THRCAD I CALCULATE ZERO ERROR THICKNESS TRANSFER RATIO TTR FROM THIS STAND TO THE DELIVERY STAND INITIALIZE UPPER LIF'IIT OF COARSE LOOP INDEX INITIALIZE EXIT INDICES OF COARSE AND VERNIER TTR= HOUTI (N)/ HOUTI (I-I) LOOPS 'ICLIO IVL=O LE .L 08 (LI-'02) INITIALIZE Do LOOP INDEX T=I NO coARsE 0R vERNIER /E% f LOOP COARSE W 5 VERNIER I DPUDFI (2) CALCULATE TRIAL DPUDFT (2)= oa FLOAT (J) ERROR CORRECTING DPUDFI(Z)-O.I *FLoATQ) DPUDF'I (I) TERF'I *01 *DPUDFI (I) PATENTEDJIIII 4 I974 T R I. -FO T I TE IAIAIII I *[LO-(POUTICA) sum 3 II? 5 START CALCULATION OF THICKNESS TRANSFER RATIO (INCLUDING TRIAL ERROR CORRECTING- TERM) FROM THIS STAND TO DELIVERY DPUDFI (2))1 STAND 2 INITIALIZE no LOOP INDEX R=3 I TTRE=TTRE INCREMENT DO LOOP CONTINUE CALCULATION OF THICK- v POUTKK) INDEX NESS TRANSFER RATIOGNCLUDING [|.0-[POUTI(K)+ m K= K+-I TRIAL ERROR coRREcTINeTERrI) *DPUDFMZ) (-I') No TTRE- TTR 0 YES NO CALCULATION COMPLETE K= ACTCNT I YES opuonmzo TTRE TTR TTR TTRE Z ERO ERROR CROSSOVER ACHIEVED CROSSOVE R NOT ACHIEVED TOO LITTLE DRAFT o0 nucII DRAF TTR-TTRE 0 YES DETECTS ZERO CROSSOVER FROFI POSITIVE VALUES INCRENENT DO LOOP INDEX 3 =3+I N0 ALL TRIALS COMPLETED 4 J=IV YES ERROR POLARITY CROSSOVER DETECTOR COARSE OR VERNIER YES LOOP IV 5 VERNIER NO COARSE INITIALIZE UPPER LII"IIT OF VERIIIER LOOP INDEX if To FIG. 2

PATENTEDJUN 191 31313308 saw u er 5 FRom F\G. 2

YES um CROSSOVER OCCUR \N NO FIRST TRlALiliiCgEr'lENT lNlTlALIZE TRIAL ERROR CORRECTlNG- DPUDFI (2) "02* DPUDFI TERM FOR vERmER LOOP FLOAT(JI)*DPUDFI (I) v BY PASS VERNIER IF r SPEED LH'HT IS 3 SPEED LIMIT ENCOUN Y TERED. TERED FLAG sET COARSE LOOP ENTRY I V 4 l0 SAVE VERN\ER LOOP I EXIT INDEX F'OR IVL=J ENGINEERING LOG CALCULATE RATIO OF DPR OJ DEVIATION TO STAND POUTI (1) PER UNIT DRAFT TO LF O4 PATENTEDJUII 4 I914 HDI (TH) STAND PER UNIT DRAFT CALCULATE NEW STAND PER UNIT DRAFTS A PDI (J) =POUTI(3)+ DPUDFI(J) YES ASSIGN DELIVERY THICKNESS AS A CONSTRAINT TO BE IIET HDKNI HOUTKN) CALCULATE NB! SETUP THICKNESS FOR REMAINING ACTIVE STANDS WORKING UP STREAT'I TOWARD SECOND ACTIVE STAND FORTHIS PASS DECREIIENT LOOP INDEX YES CALCULATE NEW DEsIRED STAND PER DNIT DRAFT 0F sEcoND AcTIvE sTAND FOR THIS PAss(TAI E-uP sTAND) NECESSARY FOR CLOSURE I NCRET'IENT DO LOOP INDEX J =3 +I T ALL ACTIVE STANDS FOR THIS NO PASS ACCOUNTED FOR 3' ACTC NT N FINISHED WITH SECOND AcTIvE NO sTAND FOR STHIS PASS HOT (2) 1 I METHOD OF ADAPTIVE THREAD BACKGROUND OF THE INVENTION This invention relates to a method of material rolling and in particular, to an improved method of adaptive thread wherein an observed deviation in per unit draft at an upstream rolling stand is compensated in the remaining stands without changing the relative per unit drafting pattern of the active downstream stands. Per unit draft of a given stand is the ratio of the input thickness minus the output thickness divided by the input thickness.

In the automated rolling of sheet material in a tan- It is also an object of this invention to provide a method of distributing observed per unit draft deviations among subsequent mill stands wherein the possibility of severe velocity transients is minimized by a more equal distribution of the per unit draft deviation among the active downstream stands of the mill.

These and other objects of this invention generally are achieved during threading of sheet material through a plurality of tandem stands of a rolling mill by detecting a deviation in the output thickness of the sheet material from one of the stands relative to the predetermined value of thickness to be produced by the predetermined per unit draft of the stand. The per unit drafts of the active downstream stands then are addem rolling mill, the rolls of the mill stands initially are l5 justed by amounts proportional to the predetermined set at predetermined spans, or roll-openings, to incrementally reduce the thickness of sheet material passing through the mill from a known incoming thickness to a desired output thickness. The roll openings for each stand initially are calculated in known fashion from variables, such as the hardness, temperature, thickness and width of the material being rolled and, since at least some of these variables cannot be known with complete certainty prior to actual rolling of the material, minor alterations often are required in the calculated mill set-up to accurately achieve the desired output thickness from themill. Because the correctness of assumed variables generally becomes known when the forward end of the strip material passes through the first active mill stand (by observing whether the stand actually produces the desired thickness reduction in the material), any observed error can be corrected by alferation of the predetermined drafts previously assigned to the downstream stands of the mill.

Observed deviations in output thickness at a stand heretofore have been corrected by distributing the corresponding per unit draft deviation among the subsequent stands of the mill in an exponentially decreasing fashion with the next active downstream stand accepting the greatest portion of the deviation correction. Although the foregoing manner of distribution has functioned successfully to produce the desired output thickness in the rolled material, large correctional adjustments applied to an adjacent downstream stand can tend to overload the stand should the stand be operating close to a constraining limit of the stand. An exponentially decreasing distribution of per unit draft correction throughout the mill also disrupts the original drafting schedule which was theoretically determined to produce optimum rolling conditions for material reductions. Moreover, should the sheet material arrive at the roll bite of the adjacent active downstream stand prior to adjustment of that stand, large roll opening corrections applied to that downstream stand can cause significant interstand velocity transients and result in poor threading of the mill.

SUMMARY OF THE INVENTION It is, therefore, an object of this invention to provide a new and improved method of distributing an observed per unit draft deviation among mill stands wherein the original drafting pattern is not significantly altered.

It is also an object of this invention to provide a method of distributing an observed per unit draft deviation among subsequentmill stands wherein the risk of exceeding stand limits is reduced.

values of the per unit drafts for the respective stands to compensate for the detected deviation in thickness without substantially altering the predetermined drafting pattern for the downstream stands. Typically, the output thickness is determined by measuring the roll force as each active stand is threaded, and using the known relationship between roll .force and thickness reduction in a stand, i.e., the thickness of incoming strip is reduced in a rolling stand In accordance with the gage meter equation:

HI HO= HI (5 F/M) wherein:

HI is the strip thickness at the input of the stand, H0 is the strip thickness at the output of the stand,

5,, is the unloaded opening between stand rolls,

F is the roll force, and

M is an empirically determined spring constant for the stand. The thickness thus determined is compared with the thickness expected from the predetermined per unit draft for the stand to arrive at the detected deviation in output thickness. The conversion from measured roll force to output thickness, the comparision of this to the expected thickness, and the percentage change required in the per unit drafts of the active downstream stands to compensate for the detected deviation in output thickness are electrically calculated in a computer. Preferably, the percentage change is determined implicitly using coarse and vernier iterative loops and the per unit drafts of the active downstream stands are calculated beginning with the delivery stand and working forward to the closure stand, the next active stand immediately downstream from the stand whereat the thickness measurement was taken.

DESCRIPTION OF THE DRAWINGS Although this invention is described with particularity in the appended claims, a more complete under- DETAILED DESCRIPTION A rolling mill 10 in accordance with this invention illustrated in FIG. 1 and generally comprises a plurality of rolling stands RSI-RS5 for incrementally reducing the thickness of strip S from an incoming thickness HI to a desired final thickness. Except for the supervisory manner of controlling screws SC l-SC5 regulating the openings between confronting work rolls WR of the stands during threading, the mill is conventional in design with the roll openings being regulated by rotation of screws SCl-SCS driven by screwdrivers SDll-SDS under the control of computer C. The lower work rolls WR of the rolling mill are each driven by an individual drive motor DMl-DMS to advance thestrip through the mill while the exit thickness of strip from rolling stand RSl is determined as described below. Load cells LCl-LCS also are provided below each stand to measure the roll force applied to the strip by the confronting rolls of the stand. Because of the known relationship between roll force and the thickness reduction in a stand, i.e., the previously referenced gage meter equation: HI HO HI (8,, F/M), it will be appreciated that the thickness of the strip from each rolling stand also can be determined from the measured roll force at that stand. In known fashion, the position of screws SC lSC5 are detected by screw position indicators SPl -SP5 to supply a screw position signal to computer C and power to drive motors DMl-DMS is measured by suitable metering devices Ml-MS to provide computer C with signals indicative of power distribution through the mill.

Computer C typically may be a conventional process control digital computer having one or two central processing units with a core memory of about 400,000 bits and a working drum memory for an additional 1 to 3 million bits of information. The computer normally also includes a card reader CR to input information relative to the order being processed, e.g., the metallurgical composition of the sheet, the desired output thickness, etc., while process information supplied to, or calculated by, the computer may be visually recorded by a typewriter or line printer LP. Computers having these characteristics are commercially available and can be obtained from General Electric Company under the trademark GE-PAC 4010 and GE-PAC 4020.

Process control information for computer C also typically would include the temperature of the strip being rolled (as measured by parameter P disposed at a suitable location along the length ofthe rolling mill) as well as the hardness, width and incoming thickness of the strip measured or calculated in conventional fashion, e.g., incoming thickness of strip S may be measured by a vertically traversable light source (not shown) and associated detector (not shown) while hardness and width typically would be input into computer C through punched cards containing such information.

At the initiation of rolling, a drafting pattern is determined for the mill andthe screw positions are calculated from the desired output thickness and known spring of the rolling stands using such input information as the hardness, temperature and width of the strip being rolled and empirically (or mathematically) determined curves of force or power per unit width as a function of the workpiece deformation. Determination of a rolling schedule for a strip is well known in the art (e.g., being disclosed in Beadle et al. US. Pat. No. Re. 26,996) and does not form a portion of the present invention.

As strip S passes through the first rolling stand of the mill (stand RS1), the thickness of the strip is reduced by the roll force applied to the strip by the confronting work rolls WR of the stand. The roll force is then measured and fed to computer C to determine. as previ ously described, the actual output thickness of the strip from stand RS1. Computer C compares the thickness thus determined with the thickness predicted from the stand for the previously determined rolling schedule.

Should there be an arror in an assumed variable, e. g.. in the hardness or temperature of strip S, an unexpected deviation dP, occurs between the per unit draft actually taken in the first rolling stand for this pass thru adaptive thread and the per unit draft calculated for the stand for. the given roll opening. This deviation will propagate through the mill causing changes dP dP,-, dP,, in the per unit drafts P P P of the succeeding active mill stands resulting in a total thickness error E expressed mathematically by the formula:

wherein: Y

P P P are the predetermined per unit drafts to be taken at stands RS RS R5,, of the rolling mill;

dP is the deviation between the draft actually taken at stand RS, and the draft assigned to the rolling stand by computer C for the chosen rolling schedule;

(1P dP,, are changes in draft propagated through the mill by the observed draft deviation dP,;

HO,, is the strip thickness at the output of the last mill stand; and,

HI is the strip thickness at the input of the stand being measured, i.e., stand RS in FIG. 1. Because strip S has not reached the successive rolling stands, i.e., RS2-RS5, the per unit drafts of these stands may be altered by computer C to correct for the observed deviation in draft at the first stand and reduce the error E to zero.

In accordance with this invention, the change in per unit draft at each downstream stand is chosen at an amount directly proportional to the predetermined per unit draft for the stand, i.e., the draft determined for the stand by computer C at the beginning of the rolling operation. Thus, the ratio of the change in per unit draft dP,, at any one stand R5,, to the predetermined draft for the stand P,, is constant and expressable by the equation (2) To compensate for the measured draft deviation, the per unit draft alterations at the downstream stands also should be opposite to the measured draft deviation at the first stand or, expressed mathematically, in absolute terms Substitution of relationships 2 and 3 into equation 1, setting the error equal to zero and expressing dP through dP,, in terms of dP- then results in the following mathematical relationship (4) Once dP has been determined from equation (4), the values of dP dP a P, can be obtained from the known relationship between the change in draft at the stand and the original draft of the stand as expressed by equation (2).

Although equation (4) can be solved explicitly for dP the stand coefficients generated in the explicit solution of the equation are complex combinations of the stand per unit drafts requiring simplifying assumptions for utilization in computer C. Solution of equation (4) without simplifying assumptions, however, can be accomplished utilizing an iterative technique such as is shown in the flow chart of HO. 2. Computer C initially will calculate the deviation (entry E as shown in'FlG. 2) in stand per unit draft by determining the difference between the expected draft at stand RS1 and that an rived at through use of the known relationship between output thickness, measured roll force, and the empirically determined spring constant for the stand. lf, subsequent to this initial calculation, a speed limit is encountered for a downstream stand (an abnormal occurrence these calculations will be repeated starting with the stand encountering the speed limit and continuing on to the delivery stand (entry E as shown in FIG. 2). In such a case, the deviation in stand per unit draft is taken as the difference between the expected draft and that value resulting from the speed limiting condition. After the deviation in stand per unit draft has been determined. an active stand number array is established beginning with the entry stand number as the first acti,ve stand ACTSTD-H). The next active stand number then becomes ACTSTD+1, etc. and terminates with the delivery stand number in the last active stand position of the ACTSTD array. Any of the remaining array elements then are filled with zeros. An example of an active stand array for three normal passes through finish adaptive thread for a mill wherein the second, seventh and eighth stands are dummied is shown in the following table: 1

FAT Pass Number Active Stand Counter ACTCNT Active Stand Number Array ACTSTD After the active stand number array and active stand counter have been initialized, computer C calculates the zero error thickness transfer ratio 'lTR from the stand being threaded to the delivery stand using the equation 'ITR (HOUTl(N )/HOUTl(l-l wherein:

HOUTl(N) is the delivery strip thickness from the mill (i.e., from RS5 of FIG. 1); and,

l-lOUTl(l-1 is the input thickness to the stand being threaded (i.e., RS1 of FIG. 1). Thus, for a thread through stand RS1, HOUTl(l-l) would be the thickness of the strip on the holding table prior to entry into stand RS1 of the finishing mill. The upper limit of the coarse loop index then is initialized along with the exit indices of both the coarse and vernier loops. Typically, a coarse loop index upper limit of five may be used together with a vernier loop index upper limit of 10. When the DO loop subsequently is indexed, a trial error correcting term DPUDFl( 2) for next active downstream stand is calculated from the formula DPUDFl(2) 0.2 FLOAT(J) DPUDFK 1) wherein:

DPUDFl( 2) is an error correcting term chosen to give closure within five attempts using multiplication factors (i.e., 0.2 FLOAT(J)) increasing in 0.2 increments; and, MM

DPUDFl(l) is the observed difference betweenthe V, expected and measured draft at stand RS1. Thus, 0.2

H FLOAT(J) is chosen as a value such that crossover would be achieved in equation (4) within the five trials designated for the coarse loop using multipliers of 0.2, 0.4, 1.0 for the product of 0.2 FLOATU). A starting calculation for the thickness transfer ratio TTRE (including the trial error correcting term) then is made from the measured stand to the delivery stand using the equation TTRE [l-(POUTl(1) DPUDFI( l [l(POUTl(2) DPUDFl(2))l terms of the thickness transfer ratio formula therefore correspond to the first two terms of equation (4). The D0loop then is indexed and the calculation of the thickness transfer ratio (including the trial error correcting term) is continued for each of the subsequent active downstream stands utilizing the formula TTRE= TTRE 1 [POUTI (K) i POUYTI (K) POUTI 2) The active stand counter then is initialized with the wherein:

number of active stands for this pass through finish d p i qt r eadste t ns W th en y. sta t POUTKK) is the expected per unit draft of active Stand R f this Pa t rq sh ssm vs th ead);

DPUDFI (2)] I POUTl(2) is the expected per unit draft of the second active stand for this pass through adaptive thread; and,

DPUDFI(2) is the trial error correcting term. After the thickness transfer ratio calculations have been completed for each of the active downstream stands, the per unit draft deviation of the first active stand for this pass through adaptive thread is tested to determine whether the draft in the stand being threaded (RS1) was insufficient or excessive. i.e., whether the zero error thickness transfer ratio TfR is greater or less than the thickness transfer ratio (including the trial error correcting term) TTRE. The difference between the zero error thickness transfer ratio and the thickness transfer ratio (including the trial error correcting term) next is calculated and if zero error should occur (a situation where the trial error correcting term DPUDF1(2) produced an exact correspondence between the thickness transfer ratio terms with and without error) computer C would directly calculate the ratio of deviation to stand per unit draft DPR according to the formula DPR [DPUDFl(2)/POUTl(2) wherein:

DPUDFl(2) is the trial error correcting term for the second active stand for this pass through adaptive thread; and,

POUTl(2) is the expected per unit draft of the second active stand for this pass through adaptive thread. Should the difference between the thickness transfer ratio and the zero error thickness transfer ratio (including the trial error correcting term) be positive (i.e., a cross-over was not achieved utilizing the calculated trial error correcting term), the DQ logp vgquld be incremented one position and the trial error correcting term would be calculated for the next higher coarse loop index, i.e., utilizing a multiplication factor of 0.4 for the O.2 FLOATU) multiplier of the trial error correcting term. Calculation of the thickness transfer ratio then continues as previously described until crossover is achieved in the coarse loop (i.e., until the difference between the trial error correcting term and the thickness transfer ratio (including the trial error correcting term) changes sign whereupon the upper limit of the vernier loop index is initialized and a determination is made of whether the cross-over occurred in the first trial increment. The trial error correcting term for the vernier loop then is chosen and the program returns to the vernier iterative loop [assuming no speed limit had been encountered (i.e., an off normal (E2) reentry)]. Should a speed limit have been encountered, an E2 reentry would be made and the computer would immediately calculate the ratio of deviation to stand per unit draft DPR in the manner previously explained.

When the program returns to the vernier iterative loop, the vernier loop is implemented in the manner previously described relative to the coarse loop until cross-over is achieved whereupon the ratio of deviation to stand per unit draft DPR is determined utilizing the formula V g g V DPR l IZPl JDFK2)/POUTl(2)l wherein: Y

DPUDFl(2) is the vernier trial error correcting term at cross-over; and,

POUTl(2) is theexpected stand per unit draft for the second active stand for this pass through adaptive thread. The DO loop next is initialized to the third active stand for this pass through adaptive thread and the changes in stand per unit draft DPUDFlU) are calculated utilizing the formula DPUDFl(J) DPR POUTl(J wherein:

and,

POUTl(J is the expected per unit draft of the Jth activestand for this pass through adaptive thread. The new per unit draft PDl(.l for each stand then is calculated from the formula PDl(.l) POUTl(J) DPUD- Fl(.l) wherein:

POUTl(J) is the output draft from stand J; and,

DPUDFKJ) is the previously calculated change in per unit draft for the respective stand. After stands 3 through N of the pass have been accounted for, the delivery thickness is assigned as a constraint to be met by the last stand of the mill and new set-up thicknesses HDIU) for the remaining active stands are calculated working upstream from the last stand towards the active stand adjacent the stand being threaded utilizing the formula wherein:

HDl(.l-l-l) is the output thickness from the next active stand immediately downstream from the stand being calculated; and,

PDl(J+l is the new per unit draft for the next active stand immediately downstream.

The decremental loop is indexed until the adjacent downstream stand, i.e., RS2 of FIG. 1, from the measured stand (i.e., RS1 of FIG. 1) is reached. At this time, the new per unit draft PDI(2) for the adjacen: downstream active stand is determined by the take-up necessary to produce closure according to the formula PDl(2) 1.0 [HDl(2)/HDl(l)] wherein:

HDI(2) is the new set-up thickness for the second active stand for this pass through adaptive thread; and,

l-lDl( l) is the actual output thickness for the first active stand for this pass through adaptive thread.

it will be appreciated that the deviation between the change in per unit'draft in the closure stand immediately downstream from the threading stand and the remaining active downstream stands will vary dependent upon the resolution chosen for the iterative loops employed to determine the percentage change in per unit draft for the stands. For example, runs having resolutions of'l in and l in 50 in the iterative loops with identical mill set-ups produced the following changes in per unit drafts in the stands While closure is effected in the adjacent stand downstream from the threading stand, it will be appreciated that any stand of the mill can be utilized as the closure DPR is the ratio of deviation to stand per unit draft;

stand depending on which stands are active and which are not.

The percentage correction of per unit draft for the rolling mill stands in accordance with this invention may be calculated by various techniques, e.g., the explicit solution of equation (4) or various computer program implementations of the flow chart of FIG. 2. One computer program written in FORTRAN for obtaining the desired per unit draft percentage correction reads as follows:

CALCULATE THICKNESS TRANSFER RATIO AS SUMING NO ERROR TTR=HOUTl(N)/HOUTI(I1 INITIALIZE CROSSOVER LOOP INDEX IV=5 CALCULATE DPUDFI(2) REQUIRED TO CANCEL ERROR DUE TO DPUDFKI) AND TO ACHIEVE THE DESIRED LOAD REDISTRIBUTION PAT- TERN 120 D0 j=l, lV

IF (IV-5) 25 GO TO 30 DPUDFI(2)=DPUDFI(2)-O. l *FLOAT(.I)*(O.2*- DPUDFI(I)) CALCULATE THICKNESS TRANSFER RATIO IN- CLUDING ERROR AND ERROR-CORRECTING TERMS no 40 K=3,N

40 CONTINUE T EST FOR ERROR POLARITY CROSSOVER IF (DPUDFKE 45, so, 50 IF ("lTRE-Tl'R) 55, so, 20 IF (TTR-TIRE) 5s, 60, 20 20 CONTINUE TEST FOR VERNIER LOOP IF (IV-5) 103, I00,

SAVE CROSSOVER LOOP EXIT INDEX AND INI- TIALIZE FOR VERNIER LOOP I ICL=J IV=IO IF(Jl) 105,105, 110 CROSSOVER VALUE OF DPUDFI(2) IS BETWEEN ZERO AND 0.2*DPUDFI( 1) DPUDFI(2)=0.0

GO TO 120 DPUDFI(2)=O.2*FLOAT(J-l*DPUDFI(1) GO TO SAVE VERNIER LOOP EXIT INDEX AND CALCU- LATE RATIO OF DEVIATION TO STAND PER UNIT DRAFT 60 IF 12.5120, no 130 IVL=J DPR=DPUDFI(2)/POUTI(2) CALCULATE DPUDFIU) AND PDI(.I) FOR AC- TIVE STANDS 3 THROUGH N FOR THIS PASS DPUDFIU )==DPR* POUTI(.I)

65 CONTINUE CALCULATE NEW DESIRED THICKNESSES HDI(N)=HOUTI(N) IF (.I-l) 70, 70, 75 CALCULATE NEW DESIRED DRAFT OF TAKE- UP STAND (SECOND ACTIVE STAND FOR THIS PASS) 70 PDI(2)=l.O(HDI(2)/HDI(l)) While the invention has been described with respect to a specific flow chart and computer program, it will be appreciated that many modifications and changes may be made in either the flow chart and/or program with out departing from the spirit of this invention. For example, it is possible to provide a direct measurement of the strip thickness from a threaded stand by suitable means, such as an X-ray gage, and to use this measurement to perform the calculations and subsequent stand adjustments as described hereinbefore. The appended claims therefore are intended to cover all modifications and variations of this invention.

What I claim as new and desire to secure by Letters Patent of the United States is:

l. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening at each stand initially is set to produce a chosen per unit draft in the sheet material to obtain a cumulative thickness reduction in said material upon passage through said mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising determining the thickness of said sheet material at the exit side of a one rolling stand, calculating the difference between the determined thickness of the sheet material from the stand and the predetermined 35 thickness to be produced by the chosen per unit draft of the stand and altering roll openings of the active stands downstream from said one stand by amounts proportional to the chosen per unit draft of the respective stands to correct for the difference between the determined and calculated thicknesses of said sheet material.

2. A method of threading sheet material through a plurality of tandem stands according to claim I wherein the proportional amount of roll opening alteration is determined by an iterative calculation in a computer.

3. A method of threading sheet material through a plurality of tandem stands according to claim 2 wherein said proportional amount of roll opening alteration is effected equally at all active stands downstream from the active stand immediately following the said one rolling stand from which said thickness difference was determined, said active stand immediately following said one rolling stand being adjusted by an amount required to completely compensate for the calculated difference in thickness.

4. A method of threading sheet material through a plurality of tandem stands according to claim 3 wherein the alterations in per unit drafts required to compensate for said difference are calculated in the computer using both coarse and vernier iterative loops.

5. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening and per unit draft values of each stand initially are chosen to obtain a desired cumulative thickness reduction in the material as the material passes hmshths l. wh in2 1 PE! rtit laf wqtastand is the difference between input and output thicknesses divided by the input thickness, said method comprising determining the output thickness from at least one of said stands to detect deviations in the determined output thickness relative to the predetermined output thickness to be produced from the stand by the chosen per unit draft, calculating the percentage change in per unit draft required for adjustment of all active downstream stands to compensate for a detected thickness deviation and adjusting the roll openings of the active downstream stands by the percentage change in per unit draft required to obtain the desired cumulative thickness reduction in the material without substantially altering the relative drafting pattern of the downstream stands.

6. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening at each stand initially is set to produce a chosen per unit draft in the sheet material to obtain a cumulative thickness reduction in said material upon passage through said mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising measuring the roll force as each active stand is threaded and using the known relationship between roll force and thickness reduction in a stand to electrically calculate the difference between the measured thickness of sheet material from thestand, thus determined, and the predetermined thickness to be produced by the chosen per unit draft of the stand and altering roll openings of the active stands downstream from the stand by amounts proportional to the chosen per unit draft of the respective stands to correct for the difference between the measured and calculated thicknesses of said sheet material.

7. A method of threading sheet material through a plurality of tandem stands according to claim 6 wherein the proportional amount of roll opening alteration is determined by an iterative calculation in a computer.

8. A method of threading sheet material through a plurality of tandem stands according to claim 7 wherein said proportional amount of roll opening alteration is effected equally at all active stands downstream from the active stand immediately following the one rolling stand from which said thickness difference was determined, said active stand immediately following said one rolling stand being adjusted by an amount required to completely compensate for the calculated difference in thickness.

9. A method of threading sheet material through a plurality of tandem stand according to claim 8 wherein the alterations in per unit drafts required to compensate for said difference are calculated in the computer using both coarse and vernier iterative loops.

10. A method of threading sheet material'through a plurality of tandem stands of a rolling mill wherein the roll opening and per unit draft values of each stand initially are chosen to obtain a desired cumulative thickness reduction in the material as the material passes through the mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising measuring the roll force as each active stand is threaded and using the known relationship between roll force and thickness reduction in a stand to electrically calculate the difference between the measured thickness of sheet material from the stand, thus determined, and the predetermined output thickness to be produced from the stand by the chosen per unit draft, electrically calculating the percentage change in per unit draft required for adjustment of all active downstream stands to compensate for a detected thickness deviation and adjusting the roll openings of the active downstream stands by the percentage change in per unit draft required to obtain the desired cumulative thickness reduction in the material without substantially altering the relative drafting pattern of the downstream stands.

11. A method of threading sheet material through a plurality of tandem stands according to claim 10 wherein the amount of roll opening alteration is calculated in a computer in an iterative fashion by solving the equation wherein:

P P P are the per unit drafts at active stands 1, 2 and n, respectively, for this pass through adaptive thread; i

dP is the measured change in the per unit draft of the first active stand for this pass through adaptive thread (an unexpected disturbance);

dP dP are the changes in'the per unit drafts of the active stands downstream from active stand 1 required to compensate for dP H0 is the output thickness of the material from the mill; and, H1 is the input thickness of the material to the first active stand for this pass through adaptive thread;

12. A method of threading sheet material through a plurality of tandem stands according to claim 11 wherein one said downstream stand is a closure stand, said closure stand being adjusted by an amount required to produce a complete correction for said detected deviation, the remaining stands of said mill being adjusted by the calculated percentage of per unit draft.

13. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening of each stand is set at a chosen value of per unit draft to obtain a desired cumulative thickness reduction in the material as the material passes through the mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising detecting deviations in the per unit draft of one said stand relative to the predetermined value of per unit draft for said stand and adjusting the per unit draft of the active downstream stands by amounts proportional to the predetermined value of per unit drafts for the respective stands to compensate for the detected deviation in per unit draft of said one stand without substantially altering the relative values of per unit draft at the downstream stands.

14. A method of rolling sheet material through a plurality of tandem stands according to claim 13 wherein the adjustment of per unit drafts is calculated in a computer in iterative fashion by solving the equation P P P are the per unit drafts at active stands 1, 2 and n, respectively, for this pass through adaptive thread;

dP is the measured change in the per unit draft of said first active stand for this pass through adaptive thread (an unexpected disturbance);

dP dP, are the changes in the per unit drafts of the active stands downstream from said first active stand required to compensate for dP H is the output thickness of the material from the mill; and,'

HI is the input thickness of the material to the first active stand for this pass through adaptive thread.

15. A method of rolling sheet material through a pluli!y.9f. !aadm a9 sot n t9 sl Hit/herein one downstream stand is a closure stand, said closure stand being adjusted by an amount required to produce a complete correction for said detected deviation in per unit draft from said one stand, the remaining active stands in said mill downstream from said closure stand being adjusted by the calculated percentage of per unit draft.

UNITED STATES PATENT OFFICE CERTIFICATE OF CORRECTION PATENT NO. 2 3, 813 ,908 DATED 3 June 4, 1974 |NVENTOR(S) I C. Michael Miglore It is certified that error appears in the above-identified patent and that said Letters Patent are hereby corrected as shown below:

Column 2, line 24, delete "In" (second occurrence) and substitute in.

Column 5 lines 1 and 2, should read as follows: [1- (P +dP 1 [l- (P +dP [1- (P (P /P X (1P [l- (P (P /P X dP (Ho /HI) Column 12 lines 20 and 21, should read as follows:

[1- (P +dP [lP +dP [1- (1 (P (P /P X dP [l- (P (P /P X dP (HO /HI) Column 13 lines 1 and 2 should read as follows:

[1- (P +dP [l- (P +dP [l- (P (P /P )X (1P [l- (P (P /P X dP (HO /HI) Signed and Scaled this sixteenth Day Of September 1975 [SEAL] Attest:

RUTH C. MASON C. MARSHALL DANN Arresting Officer Commissioner of Parents and Trademarks 

1. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening at each stand initially is set to produce a chosen per unit draft in the sheet material to obtain a cumulative thickness reduction in said material upon passage through said mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising determining the thickness of said sheet material at the exit side of a one rolling stand, calculating the difference between the determined thickness of the sheet material from the stand and the predetermined thickness to be produced by the chosen per unit draft of the stand and altering roll openings of the active stands downstream from said one staNd by amounts proportional to the chosen per unit draft of the respective stands to correct for the difference between the determined and calculated thicknesses of said sheet material.
 2. A method of threading sheet material through a plurality of tandem stands according to claim 1 wherein the proportional amount of roll opening alteration is determined by an iterative calculation in a computer.
 3. A method of threading sheet material through a plurality of tandem stands according to claim 2 wherein said proportional amount of roll opening alteration is effected equally at all active stands downstream from the active stand immediately following the said one rolling stand from which said thickness difference was determined, said active stand immediately following said one rolling stand being adjusted by an amount required to completely compensate for the calculated difference in thickness.
 4. A method of threading sheet material through a plurality of tandem stands according to claim 3 wherein the alterations in per unit drafts required to compensate for said difference are calculated in the computer using both coarse and vernier iterative loops.
 5. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening and per unit draft values of each stand initially are chosen to obtain a desired cumulative thickness reduction in the material as the material passes through the mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising determining the output thickness from at least one of said stands to detect deviations in the determined output thickness relative to the predetermined output thickness to be produced from the stand by the chosen per unit draft, calculating the percentage change in per unit draft required for adjustment of all active downstream stands to compensate for a detected thickness deviation and adjusting the roll openings of the active downstream stands by the percentage change in per unit draft required to obtain the desired cumulative thickness reduction in the material without substantially altering the relative drafting pattern of the downstream stands.
 6. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening at each stand initially is set to produce a chosen per unit draft in the sheet material to obtain a cumulative thickness reduction in said material upon passage through said mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising measuring the roll force as each active stand is threaded and using the known relationship between roll force and thickness reduction in a stand to electrically calculate the difference between the measured thickness of sheet material from the stand, thus determined, and the predetermined thickness to be produced by the chosen per unit draft of the stand and altering roll openings of the active stands downstream from the stand by amounts proportional to the chosen per unit draft of the respective stands to correct for the difference between the measured and calculated thicknesses of said sheet material.
 7. A method of threading sheet material through a plurality of tandem stands according to claim 6 wherein the proportional amount of roll opening alteration is determined by an iterative calculation in a computer.
 8. A method of threading sheet material through a plurality of tandem stands according to claim 7 wherein said proportional amount of roll opening alteration is effected equally at all active stands downstream from the active stand immediately following the one rolling stand from which said thickness difference was determined, said active stand immediately following said one rolling stand being adjusted by an amount required to completely compensate for the calculated difference in thickness.
 9. A method of threading sheet material through a plurality of tandem stand according to claim 8 wherein the alterations in per unit drafts required to compensate for said difference are calculated in the computer using both coarse and vernier iterative loops.
 10. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening and per unit draft values of each stand initially are chosen to obtain a desired cumulative thickness reduction in the material as the material passes through the mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising measuring the roll force as each active stand is threaded and using the known relationship between roll force and thickness reduction in a stand to electrically calculate the difference between the measured thickness of sheet material from the stand, thus determined, and the predetermined output thickness to be produced from the stand by the chosen per unit draft, electrically calculating the percentage change in per unit draft required for adjustment of all active downstream stands to compensate for a detected thickness deviation and adjusting the roll openings of the active downstream stands by the percentage change in per unit draft required to obtain the desired cumulative thickness reduction in the material without substantially altering the relative drafting pattern of the downstream stands.
 11. A method of threading sheet material through a plurality of tandem stands according to claim 10 wherein the amount of roll opening alteration is calculated in a computer in an iterative fashion by solving the equation (1-(P1+dP1))(1-(P2+dP2))(1-(P3+(P3/P2 X dP2)) . . . (1-(Pn+ (Pn/P2 X dP2)) (HOn/HI) wherein: P1, P2 . . Pn are the per unit drafts at active stands 1, 2 and n, respectively, for this pass through adaptive thread; dP1 is the measured change in the per unit draft of the first active stand for this pass through adaptive thread (an unexpected disturbance); dP2 . . . dPn are the changes in the per unit drafts of the active stands downstream from active stand 1 required to compensate for dP1; HO is the output thickness of the material from the mill; and, HI is the input thickness of the material to the first active stand for this pass through adaptive thread.
 12. A method of threading sheet material through a plurality of tandem stands according to claim 11 wherein one said downstream stand is a closure stand, said closure stand being adjusted by an amount required to produce a complete correction for said detected deviation, the remaining stands of said mill being adjusted by the calculated percentage of per unit draft.
 13. A method of threading sheet material through a plurality of tandem stands of a rolling mill wherein the roll opening of each stand is set at a chosen value of per unit draft to obtain a desired cumulative thickness reduction in the material as the material passes through the mill wherein said per unit draft of a stand is the difference between input and output thicknesses divided by the input thickness, said method comprising detecting deviations in the per unit draft of one said stand relative to the predetermined value of per unit draft for said stand and adjusting the per unit draft of the active downstream stands by amounts proportional to the predetermined value of per unit drafts for the respective stands to compensate for the detected deviation in per unit draft of said one stand without substantially altering the relative values of per unit draft at the downstream stands.
 14. A method of rolling sheet material through a plurality of tandem stands aCcording to claim 13 wherein the adjustment of per unit drafts is calculated in a computer in iterative fashion by solving the equation (1-(P1+dP1))(1-(P2+dP2))(1-(P3+(P3/P2 X dP2)) . . . (1-(Pn+(Pn/P2) X dP2)) (HOn/HI) wherein: P1, P2 . . Pn are the per unit drafts at active stands 1, 2 and n, respectively, for this pass through adaptive thread; dP1 is the measured change in the per unit draft of said first active stand for this pass through adaptive thread (an unexpected disturbance); dP2 . . . dPn are the changes in the per unit drafts of the active stands downstream from said first active stand required to compensate for dP1; HO is the output thickness of the material from the mill; and, HI is the input thickness of the material to the first active stand for this pass through adaptive thread.
 15. A method of rolling sheet material through a plurality of tandem stands according to claim 14 wherein one downstream stand is a closure stand, said closure stand being adjusted by an amount required to produce a complete correction for said detected deviation in per unit draft from said one stand, the remaining active stands in said mill downstream from said closure stand being adjusted by the calculated percentage of per unit draft.
 16. A method of rolling sheet material through a plurality of tandem stands according to claim 15 wherein the per unit draft deviation is determined by measuring roll force to determine the actual thickness of the material exiting each active stand of the mill at the moment of threading.
 17. A method of rolling sheet material through a plurality of tandem stands according to claim 10 wherein the output thickness deviation is determined from the speed limited value of the material thickness in the first speed limited stand of the mill. 